Question : Ram and Shyam are partners sharing profits and losses in the ratio of $\frac{7}{12}: \frac{5}{12}$ They admit Gopi as a new partner for 1/6th share, which he acquires equally from Ram and Shyam, the new profit sharing ratios of the partners will be
Option 1: 7:5:6
Option 2: 1:2:3
Option 3: 3:2:1
Option 4: 5:3:2
Correct Answer: 3:2:1
Solution : Answer = 3: 2: 1 Share of Profits given to Gopi=$\frac{1}{6}$
Share acquired by Gopi from Ram $=\frac{1}{2}$ of $\frac{1}{6}=\frac{1}{12}$ Share acquired by Gopi from Shyam $=\frac{1}{2}$ of $\frac{1}{6}=\frac{1}{12}$ Therefore, Ram's new share after surrendering $\frac{1}{12}$ Gopi's favour $=\frac{7}{12}-\frac{1}{12}=\frac{6}{12}$ Shy am's new share after surrendering $\frac{1}{12}$ in Gopi's favour $=\frac{5}{12}-\frac{1}{12}=\frac{4}{12}$ Gopi's Share $=\frac{1}{12}+\frac{1}{12}=\frac{1}{6}$ Hence, the new profit-sharing ratio of Ram, Shyam and Gopi will be : =$\frac{6}{12}: \frac{4}{12}: \frac{1}{6}=\frac{6: 4: 2}{12}$=6: 4: 2=3: 2: 1. Hence, the correct option is 3.
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